How do buffers work?

What is a buffer?

A buffer is a solution that resists a change in pH when small amounts of acid or base are added. It is composed of either a weak acid or a weak base with its respective salt.

What's going on in the buffer?

For clarity, let's use the example ethanoic acid and sodium ethanoate.

CH₃COOH _(aq) ⇌ CH₃COO^- _(aq) + H⁺ _(aq) (1)

CH₃COO^-Na⁺ _(aq) ⇌ CH₃COO^- _(aq) + Na⁺ (aq) (2)

The acid and its salt partially and reversibly dissociate, creating the above equilibriums.

What is the concentration of the buffer?

[H⁺] = (K_a[CH₃COOH]) / [CH₃COO^-Na⁺]

pH = - log([H⁺])

Note:

[acid] = mol. acid / V

[salt] = mol.salt / V

V = the total volume and so:

[acid] / [salt] = mol. acid / mol. salt

Therefore, [H⁺] = (K_a(mol. CH₃COOH)) / (mol. CH₃COO^-Na⁺)

Adding acid

The H⁺ ions react with the CH₃COO^- ions.

CH₃COOH _(aq) ⇌ CH₃COO^- _(aq) + H⁺ _(aq) (1)

Equilibrium pushed ⟵, increasing [CH₃COOH].

CH₃COO^-Na⁺ _(aq) ⇌ CH₃COO^- _(aq) + Na⁺ (aq) (2)

Equilibrium pushed ⟶, decreasing [CH₃COO^-Na⁺]

As all stoichiometric ratios are 1:1 and total volume is constant:

[H⁺] = (K_a(mol. CH₃COOH + x)) / (mol. CH₃COO^-Na⁺ - x)

where x is the number of moles of acid added. As this is a small number, there is only a negligible change in pH = - log ([H⁺])

Adding a base

The alkali neutralises the acid.

CH₃COOH _(aq) ⇌ CH₃COO^- _(aq) + H⁺ _(aq) (1)

Equilibrium pushed ⟶, decreasing [CH₃COOH].

CH₃COO^-Na⁺ _(aq) ⇌ CH₃COO^- _(aq) + Na⁺ (aq) (2)

Equilibrium pushed ⟵, increasing [CH₃COO^-Na⁺]

As all stoichiometric ratios are 1:1 and total volume is constant:

[H⁺] = (K_a(mol. CH₃COOH - x)) / (mol. CH₃COO^-Na⁺ + x)

where x is the number of moles of acid added. As this is a small number, there is only a negligible change in pH = - log ([H⁺])

Note:

K_a = acid dissociation constant

[X] = concentration of X

mol. x = moles of x

and log = logarithm base 10